Question: Simplify the following expression: $ r = \dfrac{-5}{9} - \dfrac{2x + 9}{x - 1} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{x - 1}{x - 1}$ $ \dfrac{-5}{9} \times \dfrac{x - 1}{x - 1} = \dfrac{-5x + 5}{9x - 9} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{2x + 9}{x - 1} \times \dfrac{9}{9} = \dfrac{18x + 81}{9x - 9} $ Therefore $ r = \dfrac{-5x + 5}{9x - 9} - \dfrac{18x + 81}{9x - 9} $ Now the expressions have the same denominator we can simply subtract the numerators: $r = \dfrac{-5x + 5 - (18x + 81) }{9x - 9} $ Distribute the negative sign: $r = \dfrac{-5x + 5 - 18x - 81}{9x - 9}$ $r = \dfrac{-23x - 76}{9x - 9}$